(0.04)-1.5 = ?
(0.04)-1.5 = \(\left(\frac{4}{100}\right)^{-1.5}\)
= \(\left(\frac{1}{25}\right)^{-(\frac{3}{2})}\)
= \(\left(25\right)^{\left(\frac{3}{2}\right)}\)
= \(\left(5^{2}\right)^{\left(\frac{3}{2}\right)}\)
= \(\left(5\right)^{2\times\left(\frac{3}{2}\right)}\)
= 53
= 125.
The given expression is (0.04)^-1.5. We can simplify this expression using the following formula:
a^(-n) = 1/(a^n)
where a is a non-zero real number and n is a positive integer.
Using this formula, we get:
(0.04)^-1.5 = 1/(0.04)^1.5
Now, we can simplify the expression inside the parentheses using the following formula:
a^n = (a^m)^(n/m)
where a is a non-zero real number and m and n are integers.
Using this formula with a=0.04, n=3, and m=2, we get:
(0.04)^1.5 = (0.04^2)^(3/2) = 0.0016^(3/2) = 0.000064
Therefore,
(0.04)^-1.5 = 1/(0.04)^1.5 = 1/0.000064 = 15625/1 = 125
Hence, the correct answer is option B, 125.
In summary, we used the formula a^(-n) = 1/(a^n) to convert the negative exponent to a positive exponent, and then used the formula a^n = (a^m)^(n/m) to simplify the expression inside the parentheses. Finally, we obtained the answer by taking the reciprocal of the simplified expression.
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